The student failed to consider negative values of x.
Work Step by Step
The inequality is always true when x is 0 or greater, but the inequality is not always true when x is negative. For example, let x=-3. Substitute for x and check the inequality. $3x+1\gt0$ $3(-3)+1\overset?\gt0$ $-9+1\overset?\gt0$ $-8\,/\!\!\!\!\gt0\ \ X$